Option C: The line
is the line of reflection.
Explanation:
It is given that the
across a line,
and 
Thus, the reflection is given by
⇒ 
Now, we shall determine the line of reflection.
Option A: the x-axis
To reflect the coordinates across x-axis is given by
⇒ 
Thus, the line of reflection of the coordinate L across x-axis is given by
⇒ 
This is not the equal to the given line of reflection
⇒ 
Hence, the line of reflection is not across x-axis.
Thus, Option A is not the correct answer.
Option B : the y-axis
To reflect the coordinates across x-axis is given by
⇒ 
Thus, the line of reflection of the coordinate L across y-axis is given by
⇒ 
This is not the equal to the given line of reflection
⇒ 
Hence, the given line of reflection is not across y-axis.
Thus, Option B is not the correct answer.
Option C: the line 
To reflect the coordinates across
is given by
⇒ 
Thus, the line of reflection of the coordinate L across the line
is given by
⇒ 
This is equal to the given line of reflection
⇒ 
Hence, the given line of reflection is across the line 
Thus, Option C is the correct answer.
Option D : the line 
To reflect the coordinates across
is given by
⇒ 
Thus, the line of reflection of the coordinate L across the line
is given by
⇒ 
This is not the equal to the given line of reflection
⇒ 
Hence, the given line of reflection is not across the line
.
Thus, Option D is not the correct answer.